Is Michael Atiyah right about the fine structure constant, after all?

We have in this blog tossed the idea that electromagnetic waves are in reality polarization waves of virtual pairs in space. That is, the fundamental field is the Dirac field, and photons are just phonons of the Dirac field.

The value of the fine structure constant can be expressed as

     α = k e^2 / h-bar c

The numerator in the ratio is the force between two electrons at a unit distance from each other. The denominator is the energy of a 1 Hz photon multiplied by the photon speed and divided by 2π.

If a photon is a phonon of the Dirac field, can we derive an exact mathematical formula for the above expression?

It seems to boil down to the question if the photon energy is somehow determined by the electron. The Planck constant would then depend on the properties of the electron.

Michael Atiyah this week claimed that he has derived the exact mathematical value of the fine structure constant. The author of this blog has not checked his proof, but is skeptical of its correctness.

Pair production is the process where the energy of a photon and the energy of an electron meet. If we are able to analyze pair production, we may be able to solve the question if the fine structure constant has a precise mathematical value.

In the previous blog post we raised the question what is the quantum of arbitrary energy flow in an electric field in the presence of charges. The photon is the quantum of free plane waves, it is not the quantum of energy flow in a more complex configuration.

We have coined the term quasi-photon for a photon propagating in a polarizable medium. The quasi-photon moves at a speed less than light, and, consequently, appears to have a non-zero rest mass.

What speaks against Atiyah's conjecture is that to allow the existence of atoms, there has to be flexibility in the system the electron + Planck's constant + the Coulomb force. Atoms obviously must have many possible orbits for electrons. If the physics were so tightly constrained that the Coulomb force is strictly determined, the whole system might not allow many different orbits for electrons. This argument is by no means exact. We should analyze the physical machinery more thoroughly.